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Lewis, Harry R.; Papadimitriou, Christos H. – Scientific American, 1978
Reviews the mathematical properties of algorithms and problems which can not be resolved by present methods in mathematics. (SL)
Descriptors: Algorithms, Logic, Mathematical Applications, Mathematical Logic
Download full textScandura, Joseph M.; And Others – 1975
The research reported in this paper was designed to analyze the incidence of use of higher-order rules by students solving geometric construction problems. A carefully selected set of construction problems was subjected to rigorous a priori analysis by mathematics educators to determine what basic and second-order rules might be used by able high…
Descriptors: Algorithms, Artificial Intelligence, Cognitive Processes, Geometry
Peer reviewedHostetler, Robert P. – Journal for Research in Mathematics Education, 1973
Descriptors: Algorithms, Curriculum, Elementary School Mathematics, Instruction
Groen, Guy J. – 1974
This paper presents the results of three experiments studying routine problem-solving tasks in simple addition and subtraction. Indications are that children tend to solve such problems by internalized counting procedures which may be learned independently as a consequence of practice in problem solving. Brief descriptions of exploratory studies…
Descriptors: Addition, Algorithms, Elementary School Mathematics, Mathematics Education
PDF pending restorationHiggins, Jon L., Ed. – 1976
Abstracts of 28 research reports are provided. The reports were prepared by investigators for presentation at the 54th annual meeting of the National Council of Teachers of Mathematics. A broad range of topics related to mathematics education are covered. Three reports concern the effects of differing presentations of mathematics, four are related…
Descriptors: Algorithms, Attitudes, Evaluation, Instruction
Pitt, Ruth B. – 1978
Presented is a model of problem solving that incorporates elements of hypothetico-deductive reasoning in the Piagetian sense, and heuristic-algorithmic processing in the information-processing sense. It assumes that people invoke both formal reasoning strategies and learned algorithms whenever they solve problems. The proposed model integrates the…
Descriptors: Algorithms, Cognitive Processes, Critical Thinking, Deduction
Matthews, Paul G.; Atkinson, Richard C. – 1975
This paper reports an experiment designed to test theoretical relations among fast problem solving, more complex and slower problem solving, and research concerning fundamental memory processes. Using a cathode ray tube, subjects were presented with propositions of the form "Y is in list X" which they memorized. In later testing they were asked to…
Descriptors: Algorithms, Graphs, Information Processing, Logical Thinking
Peer reviewedJones, D. A. – Mathematics in School, 1975
Basic computational problems admit several different solution algorithms. A student's choice of method may be related to personal characteristics which also bear on his ability to learn other mathematical techniques and theories. (SD)
Descriptors: Algorithms, Aptitude Treatment Interaction, Educational Diagnosis, Elementary Education
